Effect of collector molecular structure on the wettability of gold for froth flotation

Accepted Manuscript Title: EFFECT OF COLLECTOR MOLECULAR STRUCTURE ON THE WETTABILITY OF GOLD FOR FROTH FLOTATION Authors: Ivan Moncayo-Riascos, Bibian A. Hoyos PII: DOI: Reference:

S0169-4332(17)31552-0 http://dx.doi.org/doi:10.1016/j.apsusc.2017.05.197 APSUSC 36132

To appear in:

APSUSC

Received date: Revised date: Accepted date:

7-4-2017 21-5-2017 23-5-2017

Please cite this article as: Ivan Moncayo-Riascos, Bibian A.Hoyos, EFFECT OF COLLECTOR MOLECULAR STRUCTURE ON THE WETTABILITY OF GOLD FOR FROTH FLOTATION, Applied Surface Sciencehttp://dx.doi.org/10.1016/j.apsusc.2017.05.197 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

EFFECT OF COLLECTOR MOLECULAR STRUCTURE ON THE WETTABILITY OF GOLD FOR FROTH FLOTATION Ivan Moncayo-Riascosa* and Bibian A. Hoyosa

a

Departamento de Procesos y Energía, Facultad de Minas, Universidad Nacional de

Colombia Sede Medellín, Carrera 80 No. 65-223, Núcleo Robledo, 050041 Medellín, Colombia.

AUTHOR INFORMATION

Corresponding Author

*Corresponding E-mail: [email protected]

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Graphical abstract

Highlights



Molecular dynamics simulations of the collector adsorption on the gold surface.



Gold hydrophobicity alteration by collector adsorption.



Water contact angle on gold surfaces without and with collectors coating.

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ABSTRACT

Molecular dynamics simulations were conducted to evaluate the alteration of the hydrophilic state of gold surfaces caused by the adsorption of collectors with different molecular structures, using the contact angle of water droplets as an evaluation parameter. Four collectors were evaluated: SDS (with twelve hydrogenated carbon atoms), PAX (with five hydrogenated carbon atoms), DTP (with two branched aliphatic chains) and MBT (with an aromatic ring). The contact angle was evaluated for coatings of a monolayer (ML) and for surface densities of 2.89 μmol/m2 for each collector. For a ML, the hydrophobic effect generated by the aromatic ring of the MBT collector is comparable with the effect of the nonpolar short chain of the PAX collector. The increase in hydrophobicity for the gold surfaces achieved by collectors with aliphatic chains is because the water-collector interaction energy is significantly higher (repulsive) than the water-gold interactions (attractive). The lowest increase in hydrophobicity was achieved with the MBT collector, since the carbon-water interaction energy of the aromatic ring is stronger than the interaction with the carbon atoms in the aliphatic chains. The calculated contact angles of the water droplets deviated less than 4% with respect to the experimental values.

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Keywords: hydrophobicity; collector molecular structure; contact angle; gold; molecular dynamics.

1. INTRODUCTION

The use of mercury amalgam is common practice in the native gold extraction process. In this process, mercury acts as a collector that enables separation between the gold and the mineral that contains it. This practice is often artisanal and has a high impact on the health of mining personnel and the environment [1]. It is precisely for this reason that international policies are clear in the purpose of eliminating the use of mercury in the gold extraction process.

Among the many alternatives available for gold extraction, froth flotation is a particularly promising option. Froth flotation is a physicochemical method for mineral concentration and transport in water suspensions. It consists of separating solid hydrophobic particles from hydrophilic ones by injecting air bubbles. Most minerals, including gold, are hydrophilic, which is why they require the addition of collectors to increase their hydrophobicity to enable extraction through the froth phase. Collectors also reduce the water-solid interfacial tension, which facilitates the spontaneous adsorption of air bubbles, so that the particle-bubble system can rise to the surface. Once on the surface, bubbles are stabilized using frothing agents and later removed by overflow.

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Previous experimental works have provided evidence of the possibility of altering the hydrophilic state of gold surfaces by applying different substances [1], with thiosalts being the most promising collector type [1–7]. These works are oriented towards evaluating the alteration in the hydrophilic state of the gold by measuring the contact angle of water droplets on the surface, but do not provide a detailed explanation of the mechanism by which the wettability changes.

Experimental measurements have limitations, such as the variability of the measured contact angle (due to the presence of impurities, roughness and fractures on the surface) [8– 10] and scaling factors (due to the effect of the size of the water droplet) [10,11]. Also, experimental measurements do not consider the collector density on the surface, which is determined by the concentration of the collector on the impregnating solution and the impregnation time [1,7]. For these reasons, the distribution of the collectors on the surface is different for each study, and thus contact angle results for different collectors are not obtained in comparable conditions.

Molecular simulations allow us to compare the performance of collectors with different molecular structures, thereby providing the missing information from experimental practices. Additionally, molecular simulations can reveal the nature of the phenomenological process and complements the experimental work. Molecular simulations have been used to determine the alteration of the hydrophilic state of surfaces, such as graphene [12–14] and quartz [15–17]. For gold surfaces, molecular simulation studies are

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focused on the generation and tuning of the molecular potentials necessary to describe the formation and structure of self-assembled monolayers (SAMs) [18,19].

The aim of this work is to build a phenomenological model to evaluate the alteration of the hydrophilic state of gold surfaces caused by the adsorption of collectors with different molecular structures, using the contact angle of water droplets as an evaluation parameter. Five systems were constructed, the first being the initial hydrophilic state of the water-gold system, and the remaining four are associated with the measurement of the increase in hydrophobicity due to the action of the selected collectors. The collectors evaluated in this study were: (i) potassium di-isoamyl dithiophosphate (DTP) [1,7], (ii) potassium amyl xanthate (PAX) [4,20], (iii) sodium 2-mercapto-benzothiazole (MBT) [1,7] and (iv) sodium dodecyl sulfate (SDS) [21]. The first three collectors are potential candidates for froth flotation processes at an industrial level [1,4,7]. The SDS collector has never been reported to have been used in this application. However, due to its molecular structure (a thioalkane with a hydrophobic linear chain of twelve hydrogenated carbons) and its applicability for similar processes [22–24], it was selected for this study with the objective of evaluating a collector with a longer hydrophobic chain than the three previously selected. Summarizing, the selected substances allow for the determination of the effect of the molecular structure of the collector on the alteration of the hydrophilic state of gold surfaces. Contact angle results from molecular simulations were validated against experimental data reported in the literature.

2. MODEL

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The experimental evaluation of the alteration of the hydrophilic state of gold consisted of three procedures: i) clean the surface, ii) add the collector to the gold surface to allow its adsorption and iii) add water droplets to measure the contact angle. To prepare the gold surface, a solution of sulfuric acid and hydrogen peroxide was used, in order to obtain a completely hydrophilic surface at the beginning of the evaluation. Then the gold surface was impregnated with the solution of each collector with conditioning times between 5 and 20 minutes. Finally the contact angles of water droplets on the surface covered with each collector were measured to evaluate the alteration of the hydrophilic state of the gold.

The representation of the experimental procedure using molecular dynamics was performed following the sequence described above. To do this, atomistic models were used in order to describe the liquid phase of the system, which consists of water and the collector molecules. The solid phase (gold) was constructed using a wall potential. In this work, the air phase was not considered, since previous studies prove that the difference in results is statistically negligible for pressures up to 150 bar [17]

Figure 1 depicts the molecular structures of the selected collectors (DTP, PAX, MBT and SDS). All collectors are anionic, with a hydrophilic section associated with the heteroatoms in the structure (oxygen, sulfur or phosphorous) and a hydrophobic part that is related to the hydrocarbon structure.

In the DTP molecule, the hydrophobic portion of the structure consists of two aliphatic chains, with the polar core in the geometric center of the molecule (symmetrical molecular

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structure). For the PAX and SDS molecules, the polar core is located at one end of the molecule, differing from each other in chain length, which is larger for SDS (twelve hydrogenated carbon atoms) and shorter in PAX (five hydrogenated carbon atoms). The MBT molecule has an aromatic ring instead of an aliphatic chain for the hydrophobic portion of the structure.

The consistent valence force field (CVFF) potential was used to describe the collectors presented in Figure 1. This potential has been successfully used to represent systems of a similar nature [19,25]. The extended simple point charge (SPC-E) [26] potential was used to model the water molecules. This potential considers three interaction points, with a Lennard-Jones term to account for Van der Waals interactions between oxygen atoms, and a coulombic term to evaluate the electrostatic interactions of the charges located in all atoms of the molecule [15–17]. The gold surface was described using the 10-4-3 potential [27,28], which describes the solid phase as an infinitely extended and infinitely thick surface and is a function of the perpendicular distance between the surface and the atoms of the liquid phase.

The 10-4-3 potential (eq. 1) has two parameters, ϵsf and σsf, which represent the non-bond energy and size interactions of the atoms of the solid with the fluid phase, respectively [19].

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𝜎𝑠𝑓 4 2 𝜎𝑠𝑓 10 ( ) −( ) − 5 𝑧 𝑧

𝑈(𝑟𝑖𝑗) = 2𝜋𝜖𝑠𝑓 [

√2 𝑧 0.61 3 3 (𝜎 + ) 𝑠𝑓 √2 ]

(1)

This parameters are calculated using the Lorentz-Berthelot mixing rules.

𝜎𝑠𝑓 =

1 (𝜎 + 𝜎𝑓 ) 2 𝑠

(2)

1

(3)

𝜖𝑠𝑓 = (𝜀𝑠 𝜀𝑓 )2

where σs and ϵs are the Lennard-Jones length and energy parameters for the solid, respectively.

Since gold is a metal that, in this case, is interacting with ions and with the partial charges on the atoms and as in the experimental test the surface can have multiple orientations, fractures and surface defects. A way to represent the initial hydrophilic state of the gold surface is to tune the energetic parameter ϵs to give the contact angle of a single water droplet on the hydrophilic surface in order to encapsulate in its value features such as ionmetal interactions and other heterogeneities of the solid surface. This procedure is common [29–31] and it is one of the reasons why there are many values reported in the literature regarding the energetic parameter of gold, which are as wide apart as 0.02 to 6.40 kcal/mol [2,18,19,29,30]. These parameters have been used for adsorption studies of alkykthiolates [2,19], proteins [18], DNA [30] and gold-water interactions [19,29]. The energetic 9

parameter of gold, determined after the tuning procedure, is the one that characterizes the surface and it is used to calculate the gold interactions with the collectors and with water.

It should be noted that the energy parameters for Na+ (1.61 kcal/mol) and K+ (5.45 kcal/mol) are at least 10 times larger than the energy parameters of the remaining atoms of each collector. This generates a strong interaction of the ions with the solid, which allows to represent the formation of the electric double layer with atomic potentials.

The tuning procedure of the energetic parameter consists of evaluating the contact angle of a single water droplet on the surface, variating the energetic parameter of the solid phase. The value of the energetic parameter, ϵs*, which gives the contact angle closest to the experimental value (approximately 10° for the water-gold system) [31] is then determined by interpolation. To conduct this evaluation, a simulation box with dimensions of 300 x 300 x 300 Å was constructed. The wall potential 10-4-3 was placed in the bottom face of the box and a reflective wall was placed in the upper limit in order to maintain the number of water molecules. In this box, 5832 water molecules were placed, occupying a cubic space of length 55.8 Å in vacuum. Periodic conditions were used in the x and y directions.

Molecular dynamics simulations of droplet formation were conducted for 10 ns, using a time step of 1 fs in an NVT ensemble at 298 K. The contact angle was calculated from the geometric measurements of the water droplet configuration (height and radius), using a procedure developed for asymmetrical droplets [32,33]. The water droplet geometry was measured at three different times during the last two nanoseconds of the simulation (8, 9

10

and 10 ns). In each of these times, four planes were taken to measure the height and radius of the droplet.

The large dimensions of the simulation box are required to ensure that the water droplet does not interact with its images, guaranteeing at least a separation of 120 Å with the closest image (10 times the cutoff radius). In addition, the measure of the contact angle of the water droplets does not vary drastically when the number of molecules is increased beyond 5000, with variations of less than 3° with respect to simulations using 125000 molecules [33]. In previous simulations, we found that for the process of water droplets formation, the time needed to reach the 90% value of the potential energy in equilibrium, τ, is around 0.3 ns. Thus, we can be certain that a simulation time of 10 ns is large enough to ensure that the droplet is fully developed and in equilibrium, since this time is almost 30 times larger than τ. Figure S1 of the Supplementary Material shows the time evolution of the energy for the water droplet formation on the system with the SDS collector. For the other collectors, we obtained the same behavior with even smaller values of τ.

To represent the adsorption of each collector on the gold surface, the first step was an NPT simulation in order to allow the structure of the collector to relax on the surface. For this, a simulation box was constructed with the wall potential placed in the bottom face of the box, as described earlier, using the energetic parameter, ϵs*, previously obtained. Then, a single molecule of each collector, in separate simulations, was placed in the simulation box for 1 ns with a time step of 0.001 fs at 298 K and 1 atm with periodic boundary conditions in the x and y directions. The small time step is required because a single molecule is being

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represented in an NPT ensemble. With a "traditional" time step of 1 fs, the dimensions of the simulation box increase rapidly and the geometry of the molecule can be deformed, which does not allow to obtain the adsorption configuration of the collectors. At the end of this simulation. The volume and the area occupied by each collector molecule on the surface, in equilibrium state, are obtained.

Replicas of each obtained relaxed structure were placed on a gold surface of 180 x 180 Å, in order to simulate the coating on the surface. The number of collector molecules placed in the simulation box correspond to which would have a monolayer (ML) of molecules on the gold surface (depending on the size obtained for a single molecule). The collector molecules were initially placed at a distance of 4 Å above the surface. After that, an NVT simulation was conducted for 5 ns with a time step of 1 fs to obtain the adsorption configuration of a ML predicted by the molecular model.

Finally, in order to evaluate the hydrophobic state of the covered gold surface, 5832 water molecules were added to each collector system. The water droplet formation simulation was conducted by an analogous procedure to that of the system without any collector, for a total of 10 ns using a time step of 1 fs. Since the collectors promote hydrophobic surfaces, the droplets formed on the coated surface are smaller than on the initial hydrophilic surface. Thus, the size of the simulation box used in this evaluation still ensures that the water droplet does not interact with its images.

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Long range electrostatic contributions were calculated using the particle-particle-particlemesh (pppm) method [34], with a cutoff radius of 12 Å for electrostatic and Van der Waals interactions. The Lorentz-Berthelot mixing rules were used for calculating molecular interaction parameters for atoms of different species. The Nosé-Hoover thermostat and barostat were used to maintain the temperature and pressure, respectively. Simulations were conducted using parallel programing with LAMMPS [35] software. The images to determine the geometry of the droplets were generated using the VMD open-source software [36].

3.

RESULTS AND DISCUSSION

Figure S2 of the Supplementary Material shows the droplet configurations for three different values of ϵs. Water molecules are more attracted to the surface as the value of ϵs increases, which results in smaller contact angles. For ϵs = 0.6 kcal/mol, a contact angle of 90° is obtained, which indicates a hydrophobic surface. For ϵs = 1.25 kcal/mol, the resulting contact angle is 8°, a configuration close to that of a ML of water molecules, consistent with a highly hydrophilic surface. For an intermediate value of ϵs = 0.8 kcal/mol, a contact angle of 66° is obtained.

Figure 2 shows the calculated contact angle of the water droplet for values of ϵs between 1.00 and 1.25 kcal/mol. Comparing with the experimental value of 10° [31] for this system and interpolating the results obtained here, it was found that a value of ϵs* = 1.2 kcal/mol is required to properly describe the initial hydrophilic state of the gold surface.

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Figure S3 depicts the configuration of the geometry of the water droplet after 10 ns of simulation time using the calculated energetic parameter ϵs*. The measured dimensions of the droplet were h = 8.4 ± 0.1 Å and r = 86.1 ± 1.5 Å, with a contact angle of 11.1 ± 0.3°. This result shows that the selected tuning procedure gives an adequate representation of the initial hydrophilic state of the gold surface without the need for an atomistic description of the gold surface or describing, in detail, the roughness, defects and fractures.

Figure 3 depicts the adsorption configuration of each collector on the gold surface. The DTP, PAX and MBT collectors interact with the surface by means of the sulfur atom in their structure, while the SDS collector does this by means of its polar sulfate head. The results indicate that for all four cases, the collectors remain oriented with the non-polar portion of their structure parallel to the surface.

After the NPT simulation of the relaxation of a single molecule of each collector on the surface, we obtained the dimensions of the box that circumscribes each molecule and, from there, the projected area of each molecule on the surface and the number of the relaxed collector molecules necessary to cover a surface of 180 x 180 Å (which corresponds to a ML of coating). Table 1 shows the surface area occupied by each molecule of collector, the number of molecules necessary to form a ML of coating and the surface density of each collector.

The results show differences in the surface density for the collectors because its projected area on the gold surface varies according to its molecular structure. PAX and MBT

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collectors have similar sizes, and they occupy a smaller area of the gold surface and thus require a larger number of molecules to complete the ML on the surface. For SDS, in spite of having a larger chain of carbon atoms than DTP, it occupies a smaller area on the surface due to its adsorption with the shrunken aliphatic chain, while the chains of the DTP were extended on the surface.

The area of 0.216 nm2 obtained for a single molecule of PAX (with five carbon atoms in the aliphatic chain) reported in Table 1, is consistent with the results obtained experimentally and using molecular dynamics with an atomistic representation of the gold surface [37]. Reported evaluation was developed using thiolate molecules with four carbon atoms in the aliphatic chain. For Au (1 1 1) structures, reported values of 0.214 and 0.212 nm2 per molecule of thiolate were found, and for Au (1 0 0), values of 0.206 and 0.210 nm2 were found for the same molecule, experimentally and using molecular dynamics, respectively. Therefore, the surface densities obtained in this work are physically reasonable.

Figure 4 illustrates the top view of the ML formed by each collector on the gold surface. SDS and DTP exhibit a more heterogeneous coating of the surface than the PAX and MBT collectors. The steric hindrance of the aliphatic chains in the long-chained collectors causes less compact coatings.

Figure 5 shows the coordination number (which is the number molecules that a central atom holds as its nearest neighbors), obtained from the integration of the radial distribution

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function of the sulfur atoms present in each collector. These results allow for a quantitative assessment of the packing degree of the obtained coatings. Again, these results evidence different coating densities: PAX and MBT collectors have the highest surface density and DTP and SDS are the least packed. Although PAX and MBT exhibit a similar surface concentration, the coating with MBT is more heterogeneous at a local level, as can be seen from the inflexions in the curve of the coordination number. This behavior is associated with the side interactions between the aromatic rings of the MBT collector.

As previously stated, 5832 water molecules were added to each system in Figure 4 and were used to conduct the simulations of water droplet formation. Figure 6 illustrates the final configuration after 10 ns of simulation time and the contact angles calculated from the droplet geometry.

According to the experimental contact angle for water droplets on gold surfaces covered with DTP (72.3°) [1], PAX (71.6°) [4] and MBT (70.1°) [1] deviations of 3.9%, -2.2% and -1.4% were obtained, respectively. From these acceptable approximations and the predictive capability of the molecular dynamics simulations, it is expected that the value obtained for the contact angle for the system with SDS is within the same degree of approximation.

In a previous published work [33], we found that the molecular dynamics results for the contact angle of water droplets does not vary drastically when the number of molecules is increased beyond 5000. This finding is consistent with the results obtained in molecular

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dynamics studies of formation of water droplets on fluoroethylene polymers [38] and on graphite surfaces [39–41]. Additionally it has been reported [42] the contact angle calculated for water drops on polymeric surfaces has insignificant variations for drops with a radius greater than 33 Å (all radii measured in this study were larger than 50 Å). This means that, considering the number of water molecules simulated, the contact angle can be considered as an intensive property and therefore the values of contact angle obtained with simulations of small droplets are representative of macroscopic drops.

The results presented in Figure 6 show that for a ML, the SDS collector (with a longer aliphatic chain) gives a contact angle 22% higher than the one obtained with PAX (that has a short aliphatic chain), and 14% higher than the one obtained with DTP (that has branched aliphatic chains). Finally, with the MBT collector (that has an aromatic ring), the lowest contact angle was obtained, which is 24% lower than the one achieved with SDS. This indicates that the hydrophobicity of gold surfaces is favored by the use of collectors with long and linear aliphatic chains, similar to the configuration of SDS. However, generalizations in this regard must be made with caution, because in the process of altering the hydrophilic state of gold, in addition to the molecular structure of the collector, are also relevant the adsorption configuration, and the local concentration of the collector on the surface.

Figure 7 depicts the density profile for water molecules in the direction perpendicular to the gold surface. From the figure, two clearly defined peaks are distinguishable for the system without collector, which implies that the droplet consists of two layers of water molecules

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adsorbed on the surface (consistent with the small contact angle measured). At a distance of around 8 Å, the calculated density is 0.98 g/cm3, which agrees with the value of the height of the water droplet reported in Figure S3. This highly hydrophilic initial state is caused by the strong interaction between the water molecules and the gold surface.

For the surfaces covered with collectors, the water molecules are displaced from the solid surface, as is clear from Figure 7. This behavior is evidence of the alteration of the hydrophilic state of the gold surface, caused by a decrease in the water-gold interaction and the steric hindrance caused by the chemisorbed collector film.

The smaller collectors, with high surface densities (MBT and PAX), have similar water droplet profiles. In these two cases, the double-layer of water molecules is still noticeable, but to a lesser extent than the case without collector. This behavior indicates that for this coating density on the gold surface, the hydrophobic effect generated by the aromatic ring of the MBT collector is comparable with the effect of the short non-polar chain of the PAX collector.

The SDS and DTP collectors also exhibit similar density profiles for the water droplet. In these cases, small peaks are observable at distances between 4 and 5 Å from the surface, caused by a small amount of water molecules that are able to permeate the coatings, which are less compact for these two collectors. For distances above 6 Å, the density profile represents the water molecules located at the bulk of the droplet.

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Figure 8 shows the interaction energy between water molecules and the hydrophobic part of each collector. In all cases the interaction is repulsive, in contrast with the attractive interactions water-water (0.16 kcal/mol) and water-gold (1.09 kcal/mol). That is, the increase in hydrophobicity of the gold surface achieved with the collectors is due to the fact that the interaction energy between water molecules and the hydrogen and carbon atoms of the collectors is significantly higher (repulsive) than the interaction energy of water molecules with themselves (attractive). This contributes to the water molecules remaining in the bulk of the droplet.

Figure 8 also illustrates the relationship between the repulsive interaction water-collector and the contact angle of the water droplet. For the MBT collector, the lower performance is because the repulsive interaction with water molecules results be lower as the interaction of water with aromatic carbons is stronger than the interaction of water with aliphatic carbons. Thus, the total repulsion effect from the MBT collector is lower than that from the DTP, PAX, and SDS collectors.

To the hydrophobicity achieved with the SDS collector can also contribute its shrunken adsorption on the surface, which allow for a greater separation between water molecules in the droplet and the gold surface. This is evident from Figure 7, in which the density profile of the water droplet on the SDS coating indicates a separation of more than 10 Å from the surface, while for the other three collectors, the droplet is formed at around 5 Å from the surface. The increase in the separation distance between the water droplet and the surface allows for an additional reduction in the water-gold average energetic interaction.

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Alternatively, experimental studies show that the increase of the conditioning time of the gold surface with the DTP also increases the hydrophobicity [1]. This behavior can be modeled using molecular dynamics, by implementing multiple coating layers. To illustrate this, an additional simulation was conducted, using 1500 DTP molecules on the gold surface, which translates into a coating of 3 MLs.

Figure S4 of the Supplementary Material shows the contact angle for the water droplet on the gold surface covered with three layers of the DTP collector. In this case, the thickness of the coating was 28 ± 5 Å, which considerably increases the separation between the water molecules and the gold surface, and thus the contact angle of the water droplet is almost solely dependent on the water-DTP interaction. In this case, the resulting contact angle was 90.0 ± 2.4°, which gives a deviation of -3.2% with respect to the experimental value of 92.9° achieved after 20 min of surface conditioning with DTP [1].

The results presented here show that the methodology used in this study is appropriate for the evaluation of contact angles of droplets, using both a ML and multilayer coatings on the surface. On this basis, the non-structured construction of the gold surface using the 10-4-3 potential is suitable for the study of contact angle changes and for the representation of the adsorption processes of different substances.

As a comparative exercise of the performance of the four collectors evaluated with the same surface concentration, simulations with a surface density of 2.89 μmol/m2 for each collector were conducted. This is the lowest value of the coating density presented in Table

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1 (the surface density of the DTP collector). It is worth mentioning that this kind of comparison can be quite difficult to achieve experimentally.

Figure 9 shows the contact angle results considering equal surface concentrations for each collector. In this case, the SDS collector still gives the highest hydrophobicity, followed by the DTP, PAX and MBT collectors. The most relevant alteration in the results can be appreciated in the MBT collector. MLs of the PAX and MBT collectors give similar results (within 1% of the difference between them); however, when given the same surface density, the MBT collector gives a contact angle 37% smaller than that obtained with PAX. For surface densities below a ML, the effect of atomic interactions between the carbon atoms in the aromatic ring of the MBT collector and the water molecules are more relevant, since the aromatic rings are now more exposed to the interaction with water.

Experimental studies show that the contact angle generated by the collector is tightly related to the fraction of gold recovered by the froth flotation process: for a contact angle of 70°, the gold recovery is close to 65% of the gold contained in the ore material, while for contact angles close to 90°, the gold recovery increases up to 95% [1]. Therefore, although a contact angle larger than 90° is required to consider a truly hydrophobic surface, all the collectors evaluated in this study can be used in flotation processes (since they generate contact angles between 70 and 88°). However, the contact angle generated with SDS, close to 90°, makes it a promising alternative for obtaining high fractions of gold recovery.

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Finally, taking into account that the aim of this work is to build a phenomenological model of the evaluation of the contact angle of water droplets as the experimental test is performed, we consider that the models and methodologies presented are adequate for this particular type of studies. However, our study focused only on one aspect of the froth flotation process (alteration of the hydrophilic state using collectors), but there are other aspects that should be studied and that could help to better understand the phenomenon. In that sense, two interesting topics to model in a future work can be the study of the chemisorption that some collectors present on gold surfaces (simulations of this type can be performed using an all-atom representation for the gold surface and modeling the adsorption as a chemical reaction with potentials such as ReaxFF, for example), and to include the hydrodynamic aspects of the process to perform a multi-scale simulation in which the alteration of the hydrophilic state of the gold surface is studied by means of molecular simulation techniques, while models such as coarse-graining or Lattice Boltzmann Method (LBM) would allow to evaluate aspects related to the formation and stability of the froth.

CONCLUSIONS

The evaluation of collectors with different molecular structures has been carried out in order to establish the effect these structures have on the alteration of the hydrophilic state of gold surfaces, taking the contact angle of water droplets as an evaluation parameter.

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Adsorption of the SDS and DTP collectors produces more heterogeneous coatings on the surface, compared to the PAX and MBT collectors. The longer aliphatic chains of the SDS and DTP collectors generate greater steric hindrance and less compact coatings on the surface. In spite of the DSD collector having a longer aliphatic chain than DTP, it occupies a smaller surface area due to the shrunken configuration of its aliphatic chain versus the extended configuration of the DTP collector on the surface.

For a ML of coating, the MBT and PAX collectors generate similar density profiles for the water droplet. The hydrophobic effect caused by the aromatic ring in the MBT collector is comparable with the effect of the short non-polar chain of PAX. The DTP and SDS collectors also generate similar distributions of the water droplet, having a small amount of water molecules permeating through the less compact coatings of these two collectors. Deviations of the contact angle results did not exceed 4% with respect to the available experimental data in all cases.

The increase in hydrophobicity of the gold surface achieved with the collectors with aliphatic chains in their structure (DTP, PAX and SDS) is because the interaction energy between water molecules and the hydrogen and carbon atoms of the chains is significantly lower than the water-gold interaction energy and that of water molecules with themselves, which favors the water molecules remaining in the bulk of the droplet. The SDS collector (with the longest aliphatic chain) generates a contact angle 22% greater than that generated using PAX (with the shortest chain), and 14% greater than that of DTP (branched configuration). This behavior is also associated with a greater separation of the water

23

molecules from the gold surface, which implies a decrease in the water-gold interaction energy.

The smallest increase in hydrophobicity was obtained with the MBT collector (with an aromatic ring). The lower performance of this collector is explained by the interaction energy between water molecules and the carbon atoms of the aromatic ring being stronger than between water molecules and the carbon atoms in the aliphatic chains. Therefore, the net repulsion effect from the MBT collector is significantly lower than in the other cases. For surface densities below a ML, the effect of the interaction between the carbon atoms in the aromatic ring of MBT and the water molecules is more relevant, as the aromatic rings are more exposed to the interaction with water.

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Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript

Acknowledgements

Financial support for this work was provided by Agencia Nacional de Hidrocarburos (ANH) and Colciencias (call for proposals 721-2015, project 111872150012, Contract No. FP44842-016-2016). The authors also thank the Universidad Nacional de Colombia- Sede Medellín for allowing simulations in the advanced numerical computation unit (UNICA).

Ivan Moncayo-Riascos also thanks the scholarship provided by the Administrative Department of Science, Technology and Innovation – Colciencias - call for proposals 7272016.

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FIGURES

DTP

PAX

MBT

SDS

Figure 1. Molecular structures of DTP, PAX, MBT and SDS.

Figure 2. Water-gold contact angle as a function of the energetic parameter of the solid phase. The triangular points are the simulation results and the dashed line is the adjusted function for the data.

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DTP

PAX

MBT

SDS

Figure 3. Adsorption configuration of the DTP, PAX, MBT and SDS collectors. Above: top view. Below: front view. Carbon atoms are depicted as grey, hydrogen atoms as white, oxygen atoms as red, potassium and sodium atoms as purple, nitrogen atoms as blue and sulfur atoms as yellow.

DTP

PAX

MBT

SDS

Figure 4. Top view of the gold surface covered with the DTP, PAX, MBT and SDS collectors.

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Figure 5. Coordination number of sulfur atoms of the DTP, PAX, MBT and SDS collectors.

DTP

PAX

𝜃 = 75.1° ± 3.6

𝜃 = 70.0° ± 1.5

MBT 𝜃 = 69.1° ± 2.5

SDS 𝜃 = 85.7° ± 2.8

Figure 6. Contact angle of the water droplet on the gold surface covered with the DTP, PAX, MBT and SDS collectors. Carbon atoms are depicted as grey, hydrogen as white, oxygen as red, potassium as purple, nitrogen as blue and sulfur as yellow.

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Figure 7. Density profile for water molecules with and without collectors.

Figure 8. Contact angle of the water droplet and interaction energy between water and the hydrophobic part of collectors.

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Figure 9. Contact angle of the water droplet on the gold surface covered with a ML (white) and with a fixed surface density of 2.89 μmol/m2 of each collector (grey).

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TABLES

Table 1. Coating density and number of molecules to form a ML of 180 x 180 Å with the DTP, PAX, MBT and SDS collectors.

Collector DTP PAX MBT SDS

Surface area [nm2/molec.] 0.574 0.216 0.231 0.480

Number of molecules 564 1500 1402 675

Surface density [molecules/nm2] 1.742 4.630 4.337 2.083

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